Small form factor 4-mirror based imaging systems

ABSTRACT

An all-reflective optical system is described including a concave primary mirror having a central aperture and a radius, the primary mirror having one of a parabolic, non-parabolic conical, or aspherical surface, a convex secondary mirror facing the primary mirror, where an optical axis extends from a vertex of the primary mirror to a vertex of the secondary mirror, a concave tertiary mirror arranged behind the primary mirror, the tertiary mirror having one of a parabolic, non-parabolic conical or aspherical surface, a concave quaternary mirror arranged in the central aperture of the primary mirror or behind the primary mirror, the quaternary mirror having one of a spherical, parabolic, non-parabolic conical or aspherical surface, and at least one image plane having one or more aggregated sensors, wherein the image plane is positioned at a radial distance from the optical axis that is no more than the radius of the primary mirror.

INCORPORATION BY REFERENCE TO ANY PRIORITY APPLICATIONS

Any and all applications for which a foreign or domestic priority claimis identified in the Application Data Sheet as filed with the presentapplication are hereby incorporated by reference under 37 CFR 1.57. Forexample, this application is a continuation of U.S. patent applicationSer. No. 16/989,635, filed on Aug. 10, 2020, which claims priority toU.S. Provisional Application No. 62,885,296, filed Aug. 11, 2019, theentire contents of each of which is hereby incorporated by reference inits entirety for all purposes and forms a part of the presentspecification.

BACKGROUND Field

This disclosure relates generally to optical imaging systems, and morespecifically to small form factor four-mirror based optical imagingsystems for use in satellites or aerial vehicles.

Description of the Related Art

Optical imaging systems are useful in many applications such as imagingplanets or stars. Known optical system designs for satellite imaginginclude a traditional Three Mirror Anastigmat (TMA) design and a Korschdesign. Existing solutions to optical imaging have drawbacks with regardto size and corresponding resolution capability. Improvements in opticalimaging are therefore desirable.

SUMMARY

In one aspect, an all-reflective optical system is disclosed. Theall-reflective optical system comprises a concave primary mirror havinga central aperture and a radius, the primary mirror having one of aparabolic, non-parabolic conical, or aspherical surface; a convexsecondary mirror facing the primary mirror, the secondary mirror havingan aspherical surface, where an optical axis extends from a vertex ofthe primary mirror to a vertex of the secondary mirror; a concavetertiary mirror arranged behind the primary mirror, the tertiary mirrorhaving one of a parabolic, non-parabolic conical or aspherical surface;a concave quaternary mirror arranged in the central aperture of theprimary mirror or behind the primary mirror, the quaternary mirrorhaving one of a spherical, parabolic, non-parabolic conical oraspherical surface; and at least one image plane having one or moreaggregated sensors. The image plane is positioned at a distance from theoptical axis that is no more than the radius of the primary mirror.

In some embodiments, the optical system may additionally comprise anentrance pupil positioned near the primary mirror or the secondarymirror, and an exit pupil or Lyot stop positioned at one of 1) near thequaternary mirror, 2) between the tertiary mirror and the quaternarymirror, and 3) between the quaternary mirror and the image plane.

In some embodiments, the optical system may additionally comprise one ormore folding mirrors arranged to deflect rays from the quaternary mirrorto the image plane, wherein the one or more folding mirrors may beconfigured to fold a ray path. Based on using a first folding mirror,the exit pupil may be positioned between the tertiary and the quaternarymirror, or between the quaternary mirror and the first folding mirror.One of the folding mirrors may be tilted at a specific angle to anoptical axis of the system. One of the folding mirrors positioned at thefront of the image plane may widen the field of view with reflective andtransmissive sections over a same spectral range, wherein each sectionmay correspond to a specific sensor of the one or more sensors. One ofthe folding mirrors positioned at the front of the image plane mayenable simultaneous multi-color imaging, wherein the one of the foldingmirrors may be reflective over a first spectral range and transmissiveover other spectral ranges, and may be reflective over a second spectralrange and transmissive over other spectral ranges, wherein one of theaggregated sensors may be dedicated to the first spectral range and adifferent one of the aggregated sensors may be dedicated to the secondspectral range.

In some embodiments, a form factor, defined as a ratio of a distancebetween the secondary mirror and the tertiary mirror to an effectivefocal length of the optical system, may be less than 0.09. Vertices ofthe primary mirror and the secondary mirror may form an optical axis,which may be a geometric reference line extending from the vertex of theprimary mirror to the vertex of the secondary mirror. The primary mirrorand the secondary mirror may be symmetric or periodic about the opticalaxis. A diagonal of a periodic mirror may have an angle of zero degreesor 45 degrees from a diagonal of the image plane. The optical axis ofthe tertiary mirror may not coincide with a mechanical axis.

In some embodiments, a radius of the secondary mirror may be in a rangeof 1% to 3% of an effective focal length, and a radius of the tertiarymirror may be in a range of 2% to 3% of the effective focal length. Aradius of the quaternary mirror may be in a range of 6% to 22% of aneffective focal length.

In some embodiments, the folding mirrors may enable simultaneousmulti-color imaging, wherein each of the folding mirrors may bereflective over a particular spectral range and transmissive over otherspectral ranges, and wherein each added folding mirror and acorresponding one of the aggregated sensors may be associated with adifferent spectral range.

In some embodiments, a distance from the tertiary mirror to the imageplane along the optical axis may be in a range of 3% to 9% of aneffective focal length and the distance from the secondary mirror to thetertiary mirror along the optical axis may be in a range of 4% to 9% ofthe effective focal length. The system may have an imaging resolutionbetter than 1 m at a 500 km altitude.

In some embodiments, the system may be adapted to support simultaneousmulti-color imaging, including 1) panchromatic and RGB andnear-infrared, 2) visible and infrared (near-infrared, shortwaveinfrared, mid-wave infrared, or longwave infrared), 3) visible andvisible, 4) infrared and infrared, 5) UV and visible, or 6) UV andinfrared imaging.

In some embodiments, a diameter of the primary mirror may range from 3%to 8% of an effective focal length. A focal point distance from theprimary mirrors may be in a range of 1% to 6% of an effective focallength. An effective focal length may be in a range of 300 mm to 20,000mm. The optical system may further comprise a supporting structure forone or more of the mirrors. The supporting structure may be additivelymanufactured.

In some embodiments, the image plane may comprise a charge coupleddevice (CCD)-in CMOS time delay integration (TDI) sensor. TheCCD-in-CMOS TDI sensor may be a multispectral TDI, backside illuminationimager. The CCD-in-CMOS TDI sensor may comprise seven CCD arrays of4096×256 pixels each. The CCD-in-CMOS TDI sensor may comprise fourpanchromatic CCD arrays of 16384×96 pixels each and eight multispectralCCD arrays of 8192×48 pixels.

In some embodiments, the primary mirror may have a circular or anon-circular shape, the tertiary mirror may have a segmentednon-circular shape, and the quaternary mirror has a circular ornon-circular shape. The non-circular shape of the primary mirror mayenhance a modulation transfer function (MTF) and a signal to noise ratio(SNR).

In some embodiments, the quaternary mirror may face the tertiary mirrorand may be positioned to avoid interference with rays from the secondarymirror to the tertiary mirror. The optical system may additionallycomprise a supporting structure of the mirrors including a cylindricaltube or a conical baffle of the primary mirror. The four mirrors may beconstructed of zero-CTE materials, low-CTE materials, or mild-CTEmaterials, wherein the four mirrors and a supporting structure may bemade of one material. The system may be adapted to provide imaging inthe modes of starring, scanning or pushbroom, video, stereo, BRDF(Bidirectional Reflectance Distribution Function), HDR (High DynamicRange), polarimetric and low-light.

In some embodiments, the system may be adapted to be installed onboardsatellites purposed for a non-imaging mission including communicationsatellites, or installed on imaging satellites, quasi-imagingsatellites, or scientific mission satellites. The system may be adaptedto be installed onboard airplanes, drones, unmanned aerial vehicles, andballoons. A back focal length between the quaternary mirror and the atleast one image plane may be in a range of 2% to 5% of an effectivefocal length.

In another aspect, an all-reflective optical system is disclosedcomprising a concave primary mirror having a central aperture and aradius, the primary mirror having one of a parabolic, non-parabolic,conical, or aspherical surface; a convex secondary mirror facing theprimary mirror, the secondary mirror having a hyperbolic surface, wherean optical axis extends from a vertex of the primary mirror to a vertexof the secondary mirror; a concave tertiary mirror arranged behind theprimary mirror, the tertiary mirror having one of a parabolic,non-parabolic, conical and aspherical surface; a concave quaternarymirror arranged in front of the central aperture of the primary mirror,the quaternary mirror having one of a spherical, parabolic,non-parabolic, conical or aspherical surface; and at least one imageplane having one or more aggregated sensors, wherein the image plane ispositioned at a radial distance from the optical axis that is no morethan the radius of the primary mirror.

BRIEF DESCRIPTION OF THE DRAWINGS

Elements in the figures have not necessarily been drawn to scale inorder to enhance their clarity and improve understanding of thesevarious elements and embodiments described herein. Furthermore, elementsthat are known to be common and well understood to those in the industryare not depicted in order to provide a clear view of the variousembodiments described herein, thus the drawings are generalized in formin the interest of clarity and conciseness.

FIGS. 1A and 1B are schematics of an embodiment of an optical systemthat may be used for imaging.

FIGS. 1C and 1D are schematics of another embodiment of an opticalsystem that may be used for imaging.

FIGS. 1E and 1F are schematics showing diagonals for respectively aperiodic mirror and an image plane.

FIGS. 1G and 1H show example embodiments of optical systems having aperiodic primary mirror.

FIG. 2A is a block diagram showing a schematic of an embodiment of apayload system for a satellite that may include the various opticalsystems described herein.

FIG. 2B is block diagram showing a schematic of an embodiment of animage plane circuit that may be used with the various optical systemsdescribed herein.

FIGS. 3-5 are schematics showing various embodiments of configurationlayouts for mirrors and an imaging plane that may be used with thevarious optical systems described herein.

FIGS. 6-9 are schematics showing various embodiments of configurationlayouts for mirrors, including one or more folding mirrors, and animaging plane, that may be used with the various optical systemsdescribed herein.

FIGS. 10-13 are schematics showing various embodiments of configurationlayouts for mirrors, including one or more folding mirrors, and twoimaging planes, that may be used with the various optical systemsdescribed herein.

FIGS. 14A-14D are various views of an embodiment of a camera system thatincludes the optical system of FIG. 1 .

FIGS. 15A-17B are graphical plots showing various embodiments ofperformance characteristics for the optical system of FIG. 1A.

FIGS. 18A-20B are graphical plots showing various embodiments ofperformance characteristics for the optical system of FIG. 1C.

FIGS. 21A and 21B are graphical plots showing distortion performancefor, respectively, the optical systems FIGS. 1A and 1C.

DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS

In the following discussion that addresses a number of embodiments andapplications, reference is made to the accompanying drawings that form apart hereof, and in which is shown by way of illustration specificembodiments in which the embodiments described herein may be practiced.It is to be understood that other embodiments may be utilized, andchanges may be made without departing from the scope of the disclosure.

Various inventive features are described below that can each be usedindependently of one another or in combination with another feature orfeatures. However, any single inventive feature may not address all ofthe problems discussed above or only address one of the problemsdiscussed above. Further, one or more of the problems discussed abovemay not be fully addressed by the features of each embodiment describedbelow.

Described herein are embodiments of small volume, high resolutionoptical imaging systems and methods that can be used in satellites andother aerial systems. An optical system 100 is shown in FIGS. 1A and 1 sone embodiment that may be used for providing high resolution imagingperformance in a “micro” or small form factor (volumetric envelope). Theoptical systems may “piggyback” on other missions with existing highbandwidth capabilities.

A constellation of satellites in orbit may operate in collaboration witheach other for coordinated ground coverage. The orbits of the satellitesin the constellation may be synchronized. For example, the orbits may begeostationary, where the satellites may have orbital periods equal tothe average rotational period of Earth and in the same direction ofrotation as Earth. Or the orbits may be sun-synchronous, such as anearly polar orbit around Earth, in which the satellite passes over anygiven point of the Earth's surface at the same local mean solar time orthe orbit precesses through one complete revolution each year so italways maintains the same relationship with the Sun. Synchronous systemsintroduce complexity by requiring dedicated platforms and sensors,launchers, and operation stations. For remote sensing, typical examplesof such synchronized constellations include the programs of PLANETSCOPE(a.k.a. DOVE), SKYSAT, BLACKSKY, and CARBONITE.

The systems described herein may be used in systems in synchronous aswell as asynchronous orbits. Thus, in some embodiments, the imagingsystems may be used with an Asynchronous Constellation of Earthobservation Camera system (ACEC). This is especially true forconstellations of many small satellites, such as CUBESATs, and also withLow-Earth Orbit (LEO) broadband data relay satellite constellations,such as Space NGSO Satellite System, One Web, and Amazon's KUIPERSystem. Any of the optical systems or features thereof described hereinmay include any of the features of the micro optical and camera systemsand other aspects described in “Study on the feasibility of micro camerasystems for asynchronous, gigantic satellite constellation”, by YoungwanChoi, Proc. SPIE 11127, Earth Observing Systems XXIV, 111270Z (9 Sep.2019, available at https://doi.org/10.1117/12.2529090), the entirecontents of which are incorporated by reference herein in theirentirety.

An asynchronous constellation may include camera systems onboard anyavailable platforms, which have planned missions but can host additionalpayloads. It may be different from the nominal constellation in thesense that it will not be operated synchronously and not providecoordinated ground coverage with the sole purpose of only providing astream of images. The most significant benefit of the asynchronousconstellation is to avoid or minimize cost, time, and effort to developa platform, require a specific launch system, and operate a dedicatedground control system, which can be a large fixed cost. An advantage ofleveraging LEO broadband data relay satellites for asynchronousconstellation imaging is its broad data bandwidth. CUBESATs or otherplatforms with dedicated imaging or other missions may suffer fromdecreased data bandwidth. Free from the data bandwidth issue,asynchronous constellation with the LEO data relay satellites can streamimage data in dedicated channels as the satellites stream movies orother content so that users can selectively receive, record, and processimage data.

To do this, much smaller or micro camera systems that have dimensionaladvantages and can accommodate themselves to any available space areneeded. Recent developments of smaller cameras focuses on dimensionaladvantages only so that such development relies on optical designs thatare easier to design, simpler to develop, or cheaper to build. However,such an approach may seem reasonable but may put a limit or constrainton leveraging such cameras for serious missions due to decreasedperformance, such as optical resolution.

The optical system 100 and the other embodiments of imaging systemsdescribed herein may be used for constellation operations and be microin physical dimension as well as be advanced in performance. Systems andmethods for a 4-mirror telescope in a small form factor are described.

The embodiments described herein may be onboard satellite platforms thatare already planned, as a secondary payload or an additional system. Insome embodiments, the imaging system may have a size on the scale of astar sensor or tracker. The imaging system may be lightweight. Theimaging system may minimize power consumption. The imaging system andits interface to a platform may be simple so that it can be installedand operated easily. The imaging system may be capable of properimaging, which may be described by its specification. The imaging systemmay have proper MTF values. The imaging system may be designed tooperate over a wide spectral range and equipped with a number ofchannels over the spectral range, with panchromatic, red, green, blue,and near infrared as a baseline set. The imaging system may be capableof a large field of view.

For such a camera system, an important requirement is distortionproperty. A camera system with a small f-number, a small aperture with alonger effective focal length for higher resolution, may need atime-delay-integration (TDI) sensor to achieve a proper signal-to-noiseratio (SNR) for further processing on the ground. Distortions induced byoptical design can cause smear in the camera system. To avoid asignificant degradation of image quality for TDI imaging, distortionsinduced by the system should be minimized over an entire field-of-view(FOV).

The optical imaging systems described herein are based on a reflectiveor mirror system, which may be unusual for a small form, affordablesystem. Usual cameras for CAN- or NANO-SAT are based on a cata-dioptricdesign for its design simplicity and cost reduction. The examples arePLANETSCOPE (a.k.a. DOVE), SKYSAT, BLACKSKY, and CARBONITE.

The design of the SKYSAT camera is based on a Ritchey-Cassegraintelescope, which has two mirrors (primary and secondary) and a smallnumber of lenses. It is known for easy manufacturing, cost reduction,and simple alignment/assembly logic. Also, it utilized COTS frame CMOSsensors. The CARBONITE camera is an example of commercially available,off-the-shelf astronomical telescope, which is modified to beaccommodated to space environment, and equipped with a commercial CMOSsensor for color video imaging. Utilizing a commercial telescope seemedto be a smart move in a sense that development or manufacturing effortcan be reduced, cost can be cut seriously, and operation management canbe efficient. Whole processes were developed suitable for implementingconstellation of Earth observation satellites.

Different from those approaches, the optical system embodimentsdescribed herein for cameras are based on a reflective design that is afour-mirror system. The optical system described herein may have nolimit of spectral range to be covered. The system may have no chromaticaberration, which can be critical for multispectral imaging. The systemmay have high design flexibility due to degree of freedom ofmulti-mirror system. The system may have mass reduction deduced bymirror light-weighting. The system may have a small form factor.

FIG. 1A is a perspective schematic view of an optical layout of a firstoptical system 100 showing optical path lines. FIG. 1B is a perspectiveschematic view of the optical system 100 without the optical path linesshown for clarity. The optical lines may be indicative of multiplespectral bands. Referring to FIG. 1C, a perspective view of an opticallayout of a second optical system 150 showing optical lines isillustrated. FIG. 1D shows the optical system 150 without the opticallines for clarity.

The first two mirrors of the optical systems 100, 150, a primary mirror104 and a secondary mirror 105 in FIGS. 1A and 1B, and a primary mirror154 and a secondary mirror 155 in FIGS. 1C and 1D, are responsible forpower of the systems so that it can determine its effective focal lengthor resolution. “Effective focal length” as used herein has its usual andcustomary meaning, and includes without limitation the distance from aprincipal plane of an optical mirror to an imaging plane 118, 168.Entrance pupil 124 of the optical system 100 (shown in FIGS. 1A and 1B),and entrance pupil 174 of the optical system 150 (shown in FIGS. 1C and1D), control the amount of light through the respective systems, and maybe located at the respective primary mirrors. The entrance pupil may bethe optical image of the physical aperture stop, as seen through thefront (the object side) of the optical system. The corresponding imageof the aperture as seen through the back of the optical system is calledthe exit pupil.

The primary mirrors 104, 154 may be supported by a structural support102 having radially extending beam 103 to support the mirror structure.The structure 102 and beams 103 may minimize the distortion on theprimary mirror surface that may be induced by bonding and thermalenvironmental change. Also, it may protect the primary mirror fromrandom vibration and shock that the camera may experience during launch.

In some embodiments, the various mirrors and supporting structures forany of the optical systems described herein may be formed of aluminum,ceramics, designed composite materials, other suitable materials, orcombinations thereof. In some embodiments, the one or more structuresand/or the one or more mirrors can be manufactured by 3D printingtechnology also known as additive manufacturing technology. For example,the mirrors and the supporting structure may all be additivelymanufactured as one monolithic piece.

A tertiary mirror 113 in FIGS. 1A and 1B, and a tertiary mirror 163 inFIGS. 1C and 1D, contribute to widening a field of view (FOV) andcorrects corresponding residual optical aberrations. The tertiarymirrors 113, 163 may not include an optical axis, for example forsimpler manufacturability, and two or more tertiary mirrors may bemanufactured from one base piece. A quaternary mirror 114 in FIGS. 1Aand 1B, and a quaternary mirror 164 in FIGS. 1C and 1D, may minimizedistortion and control a back focal length. “Back focal length” as usedherein has it usual and customary meaning, and incudes withoutlimitation the distance between the last surface of an optical mirror toits image plane. The fields of view of the optical systems 100, 150 aredesigned so that the rays do not interfere with the respectivequaternary mirror and the central aperture of the respective primarymirror. The quaternary mirrors 114, 164 reflect the respective lightalong the optical path to the imaging plane 118, 168.

FIG. 1D shows the second optical system 150 but without showing theoptical path lines for clarity. The diameter of the aperture or centralhole 110 in FIG. 1B and 160 in FIG. 1D is minimized to maximize the usearea of the primary mirror and in some embodiments is not larger thanthe corresponding secondary mirror 105, 155. The diameter of the centralhole 110 in FIG. 1B and hole 160 in FIG. 1D may be designed large enoughto not interfere with the light rays travelling through the centralholes 110 and 160.

The primary mirrors 104, 154 and/or the secondary mirrors 105, 155 maybe symmetric or periodic about the respective optical axis. FIGS. 1E and1F are schematics showing diagonals for respectively a periodic mirrorand an image plane. The diagonal of a periodic mirror may have an angleof zero degrees or 45 degrees from a diagonal of the image plane. Theoptical axis of the tertiary mirror may not coincide with a mechanicalaxis.

FIGS. 1G and 1H show example embodiments of optical systems 170, 190respectively having a periodic primary mirror 174, 194. The opticalsystems 170, 190 further include, respectively, a secondary mirror 175,195, a tertiary mirror 173, 193, a quaternary mirror 184, 198 and animaging plane 189, 199. The optical systems 170, 190 may have the sameor similar features and/or functions as the optical systems 100 or 150.

The optical systems 100, 150 may include any of the same or similarfeatures and/or functions as the other embodiments of optical systemsdescribed herein, and vice versa. For example, the optical systems 100,150 may include any of the same or similar features and/or functions asoptical systems 210, 300, 400, 500, 600, 700, 800, 900, 1000, 1100,1200, 1300, 1430, 1460, and vice versa. For example, for any of theoptical systems described herein, the primary mirror may be concave andhave a central aperture.

The primary mirror may have a parabolic surface, a non-parabolic conicalsurface, or an aspherical surface. A “parabolic surface” as used hereinhas its usual and customary meaning, and includes, without limitation, areflective surface used to collect the light energy and may have a shapethat is part of a circular paraboloid, that is, the surface generated bya parabola revolving around its axis. A “non-parabolic conical surface”as used herein has its usual and customary meaning, and includes,without limitation, a curve rotated about its axis where the curve isobtained as the intersection of the surface of a cone with a plane otherthan a parabola. For example, the “non-parabolic conical surface” may behyperbolic, elliptical, or circular. An “aspherical surface” as usedherein has its usual and customary meaning, and includes, withoutlimitation, a surface that is not spherical. In some embodiments, aspherical surface may be slightly altered so as to reduce sphericalaberration.

The secondary mirror may be convex and face the primary mirror. Thesecondary mirror may have an aspherical surface. The tertiary mirror maybe concave and arranged behind the primary mirror. “Behind” may refer toa side of the primary mirror that is opposite the side of the primarymirror that reflects incoming light to the secondary mirror. Thetertiary mirror may have a parabolic surface, a non-parabolic conicalsurface, or an aspherical surface. The quaternary mirror may be concaveand arranged in the central aperture of the primary mirror, before theprimary mirror or behind the primary mirror, for example as shown inFIG. 3 . The quaternary mirror may have one of a spherical surface, aparabolic surface, a non-parabolic conical surface, or an asphericalsurface.

There may be at least one image plane having one or more aggregatedsensors, where the image plane is positioned at a specific distance froman optical axis. The optical axis may be defined as a geometricreference line extending between the vertices of the primary andsecondary mirrors. The vertex for a given mirror may be a point on themirror's surface where the principal axis meets the mirror.

The optical system 100 may have a larger primary mirror 104 and thushigher resolution relative to the primary mirror 154 of the opticalsystem 150. The resolution of the optical system 100 may be better than1 m at 500 km altitude. The optical system 150 may have a resolution ofbetter than 2 m at 500 km altitude. The optical system 150 may have alarger field of view (FOV) than the optical system 100. The opticalsystem 100 may have a narrower field of view (FOV) relative to theoptical system 150. The optical system 100 may have volumetricdimensions of 200 mm (W)×200 mm (H)×250 mm (L). The optical system 150may have volumetric dimensions of 100 mm (W)×100 mm (H)×150 mm (L). Theoptical system 150 may be lighter in weight than the optical system 100.The optical systems 100, 150 may both have a proper MTF for higherresolution imaging.

Both the optical systems 100, 150 may have similar mirror types andoptical paths. But their respective purposes and missions may bedifferent. The purpose of the optical system 100 may be to map thesurface of the Earth and acquire geospatial data. The purpose of theoptical system 150 may be for remote sensing and environmentalmonitoring.

In some embodiments, the optical systems 100, 150 may achieve variousparameters for orbital systems and/or imaging systems. Exampleparameters achievable with the optical systems 100, 150 are described inTable 1. For example, the design orbit may be set to 500 km, thespectral bands may be designed to be compatible with big satellites andscientific satellite imaging except the panchromatic band, etc. Thepanchromatic band (PAN band) may be designed to include up to red-edge,improving Modulation Transfer Function (MTF) in the band, which may beunavoidable due to its small aperture size.

TABLE 1 Optical Optical Design Parameters System 100 System 150 OrbitAltitude (km) 500 500 Ground Sample Distance (GSD, m) ≤1 ≤2 SpectralRange (nm) PAN band 450~720 450~720 NIR band 770~890 770~890 Red band630~690 630~690 Green band 520~590 520~590 Blue band 450~520 450~520Pixel size (μm) 5 5 Number of active pixels ≤12000 ≤8000 Size of ClearAperture (mm × mm) ≤200 × 200 ≤100 × 100 Time-Delay-Integration (TDI)steps of 128 128 Backside-Illumination (BSI) sensor

FIG. 2A is a block diagram of an example payload system 200configuration for an optical system 210 in a satellite. The opticalsystem 210 is shown in schematic form. The optical system 210 includes aconcave primary mirror 204 having a central aperture 212. The primarymirror may have one of parabolic, non-parabolic conical or asphericalsurface. A smaller convex secondary mirror 205 faces the primary mirror204 and has an aspherical surface. The secondary mirror may have anaspherical surface. A concave tertiary mirror 213 is arranged behind theprimary mirror 204. The tertiary mirror may have one of parabolic,non-parabolic conical or aspherical surface. A concave quaternary mirror214 is arranged slightly behind the central aperture 212 of the primarymirror 204, where the quaternary mirror can have one of a spherical,parabolic, non-parabolic conical or aspherical surface. The primarymirror 204, the tertiary mirror 213 and the quaternary mirror 214 eachhave positive power or focal length, and the secondary mirror 205 hasnegative power. “Behind” may be defined as described above. Behind mayalso refer to a direction in FIG. 2A as oriented that is to the right,such that “behind” the primary mirror 204 may mean to the right of theprimary mirror 204 as oriented in the figure.

An image sensor 216 having up to ‘n’ aggregated sensors that convertlight into electrical signals is positioned behind the primary mirror204. In certain embodiments, the image sensor 216 may deliver an outputformat of thirty-two sub-LVDS (low-voltage differential signaling)channels of digital data across an interface 218 to a control andprocessing electronics portion 220 of the satellite. In otherembodiments, other output formats are used. The sensor 216 includes areadout integrated circuit (ROIC) used for infrared, visible, and otherarrayed sensors. The functions supported by the ROIC include processingand shaping of an image signal and may include unit cell preamplifiers.Interface 218 also includes control signals from the control andprocessing electronics 220, where the control signals may include aserial peripheral interface (SPI) and a clock signal in someembodiments.

In certain embodiments, a data formatting and distribution subsystem 224receives the data across the interface 218 and then further sends thedata to a data processing with machine learning subsystem 226 and to adata storage and archiving subsystem 230 to be stored. The stored datafrom the data storage and archiving subsystem 230 can be sent directlyto the data processing subsystem 226 for various types of processing.The output of processed data from the data processing subsystem 226 canbe sent directly to the data storage and archiving subsystem 230 forstorage. The output of processed data from the data processing subsystem226 and data from the data storage and archiving subsystem 230 can besent to a data formatting, encryption and transmission subsystem 228.The output of the data formatting, encryption and transmission subsystem228, such as image data, is then sent to a satellite Bus for furtherdistribution, which may include transmission to an earth station, relaysatellite, or other entity that receives the data. The data processingsubsystem 226 may include one or processors and one or more memories,such as a memory for program instructions and a memory and/or a cachefor data.

A payload control electronics subsystem 222 receives telecommands fromthe satellite Bus and provides housekeeping data to the satellite Bus.The payload control electronics subsystem 222 provides commands toportions of the payload system 200, including to the image sensor 216and/or to a thermal control, temperature data and optical focusingsubsystem 234. The thermal control, temperature data and opticalfocusing subsystem 234 provides control signals, such as thermal controland optical focusing, via an interface 232 to the optical system 210 andreceives temperature data back from the optical system 210.

A power conversion, distribution and telemetry subsystem 236 receivestelecommands from the satellite Bus and provides telemetry data to thesatellite Bus. The power conversion, distribution and telemetrysubsystem 236 may also receive power, such as from solar panels orbatteries of the satellite.

An important issue with imaging systems for smaller satellites, such asCUBESATs, is calibration, including absolute and inter-sensorcalibrations. Most imagery from commercial CUBESATs is not calibrated ina standard way on a standard radiance or reflectance scale, for example.Thus, it may be challenging to compare the image data with bigcommercial satellites or scientific satellites imaging, like MODIS orLANDSAT. Even inter-sensor calibration is uncertain, which may owemainly to temporarily unstable or inconsistent performance of commercialsensors.

On the contrary, the sensors for the optical systems described herein,such as the aggregate sensor of the sensor 216 in optical system 210,may be developed and tailored to space applications and theirconsistency and stability may be validated. Importantly, the opticalsystem 210 and all the optical systems described herein may becalibrated according to the standard processes and with respect to eachother so that all the image data from the systems is compatible witheach other and also with reference systems.

Referring to FIG. 2B, an example embodiment of a sensor circuit for theimage sensor 216 is shown. The image sensor 216 may include a readoutintegrated circuit (ROIC) 272 and a charged coupling device (CCD) array270. Photons incident on the surface of the CCD array 270 (top surfaceas oriented in the figure) generate a charge that can be read byelectronics and turned into a digital copy of the light patterns fallingon the device. In certain embodiments, a charge coupled device incomplementary metal-oxide-semiconductor (CCD-in-CMOS) time delayintegration (TDI) sensor from IMEC International may be used for theoptical system 210, even though a pixel size of 5 micrometers (μm) ispreferred. In some embodiments, using a format of 4096 columns and 256stages per multiband CCD array 270, a backside illumination sensorcombines a TDI CCD array with CMOS drivers and readout pixels on a pitchof 5.4 μm. An on-chip control and sequencer circuit may be included. Incertain embodiments, a 130 MHz clock 262 may be an input to the imagesensor along with a serial peripheral interface (SPI) for control. Theimager may interface through the SPI and may integrate on-chip PLLs todeliver an output format of 32 sub-LVDS (low-voltage differentialsignaling) channels as part of the ROIC 272. A seven-band version of thecircuit can contain seven CCD arrays of 4096×256 pixels each.

In other embodiments, other sensor circuits may be used for the imagesensor 216, which may have differing sizes of the array 270 and adifferent ROIC 272 for the output of data. For example, the image sensor216 may include four panchromatic CCD arrays of 16384×96 pixels each andeight multispectral CCD arrays of 8192×48 pixels.

To maximize the area that is exposed to light, backside illuminationtechnology can be used. This consists of bonding the sensor wafer to acarrier wafer and thinning it from the backside. This directly exposesthe CCD gates to the light, without obstruction of metal lines. Aneffective fill factor thus reaches 100% percent. Backside illuminatedCMOS imagers feature a very high intrinsic light sensitivity and arevery efficient in detecting (near) ultraviolet and blue light. Severalantireflective coatings (ARCs) are available to reach a high quantumefficiency in selected regions of the spectrum, e.g. more than 70% inthe UV range or more than 90% in the visible range.

With a TDI sensor, image quality is sensitive to platform motion, whichcan be represented by image smear MTF. The image smear MTF of theoptical system 210 may be 0.974 with smearing of 0.2 pixels, the numberof TDI steps at 128, and a clocking phase of 4. This may imposerequirements of attitude stability of the platform, which may betwenty-two micro-radians per second (μrad/sec) or 4.54 arcseconds persecond (arcsec/sec). When the attitude stability requirement is relaxedto smearing of one pixel, then the smear MTF becomes 0.75 and thestability may be 23 arcsec/sec.

Referring to FIG. 3 , a schematic of an embodiment of an all-reflectiveoptical system 300 is shown. The optical design of the optical system300 may be different from a traditional Three Mirror Anastigmat TMA orthree mirror Korsch design. The Korsch design may have an ellipsoidsurface for the primary mirror, a hyperbola surface for the secondarymirror, and an ellipsoid surface for the tertiary mirror.

The optical system 300 includes a concave primary mirror 304 having acentral aperture 310, where the primary mirror can have one of aparabolic, non-parabolic conical, or aspherical surface. A smallerconvex secondary mirror 305 faces the primary mirror 304 and has anaspherical surface. A concave tertiary mirror 313 is arranged behind theprimary mirror 304, where the tertiary mirror can have one of aparabolic, non-parabolic conical or aspherical surface. A concavequaternary mirror 314 is arranged in front of the central aperture 310of the primary mirror 304, where the quaternary mirror can have one of aspherical, parabolic, non-parabolic conical or aspherical surface. Theprimary mirror 304, the tertiary mirror 313 and the quaternary mirror314 each have positive power or focal length, and the secondary mirror305 has negative power.

An image plane 316 having one or more aggregated sensors that convertlight into electrical signals is positioned behind the primary mirror304. In certain embodiments, the image plane 316 is positioned at aspecific distance from an optical axis that is defined by a mechanicalsymmetry around a line through the vertices of the primary and thesecondary mirrors, which may define the “optical axis.” The specificdistance is within the physical radius (from the optical axis) of theprimary mirror. Thus, the image plane will not exceed a cylindricalenvelope that is defined by the radius from the optical axis of theprimary mirror. The radius of the primary mirror may extendperpendicularly from the principal axis of the mirror to an outermostedge of the mirror. The principal axis may be a geometric reference linegoing through the center of the mirror that is exactly perpendicular tothe surface of the mirror.

The optical system 300 uses the secondary mirror 305 that is symmetricaround the optical axis. The tertiary mirror 313 can have a segmentednon-circular shape. The quaternary mirror 314 can have a circular ornon-circular shape. The primary mirror 304 can have a circular or anon-circular shape, where the latter is to enhance modulation transferfunction (MTF) and signal to noise ratio (SNR). A circular shape isinscribed to a non-circular shape, which may be periodic about theoptical axis.

For an example of a square and its incircle, the incircle may be theshape of a primary mirror for traditional optical system design. If theradius of the incircle is “r,” then the area of the square will belarger by 4/pi. This is not usually an issue for a larger camera forwhich a large volume is allocated. However, for a small satellite, whichis usually a cuboid, a primary mirror in a square shape can have alarger area by 4/pi and boost MTF and SNR.

Both Korsch and other four-mirror optical designs do not use a parabolicsurface for the primary and/or the tertiary mirrors. With the primaryand/or the tertiary mirrors of the optical system 300 having a parabolicsurface, the optical system 300 can provide a unique, affordablesolution to a mission with budget constraints. For a parabolic surface,a general test setup can be used for manufacturing, or a stitchingmeasurement is possible. Also, a commercial product line can be used forparabolic mirror manufacturing, especially when mirrors are smaller than300 mm. In contrast, non-parabolic conic or aspherical surface mayrequire a dedicated test tool, including computer generated hologram(CGH) or nulling optics.

For a parabolic surface, a general test setup can be used formanufacturing, or stitching measurement is possible. Also, a commercialproduct line can be used for parabolic mirror manufacturing, especially,when mirrors are smaller than 300 mm.

The primary and the secondary mirrors 304, 305 forming the optical axisare symmetric or periodic about this axis. The primary and secondarymirrors face each other. The tertiary mirror 313 faces the back of theprimary mirror 304 and may be a segmented mirror. As used herein,“segmented mirror” includes its usual and customary meaning andincludes, without limitation, an array of smaller mirrors designed toact as segments of a single, larger curved mirror. The optical axis ofthe tertiary mirror 313 may not coincide with a mechanical axis. As usedherein, the “mechanical axis” has its usual and customary meaning, andmay includes, without limitation, a normal vector at the center or atthe edge of the mirror. In certain embodiments, the tertiary mirror 313is a segment of a larger mirror. In such embodiments, the optical axisfor the tertiary mirror 313 may refer to the optical axis of the largermirror and the mechanical axis may refer to the axis of the segmentedmirror. The quaternary mirror 314 faces the tertiary mirror 313 and ispositioned to avoid interference with rays from the secondary mirror 305to the tertiary mirror 313.

The metering and supporting structure of the mirrors can be acylindrical tube or a conical baffle of the primary mirror 304, such asthose shown and described with respect to FIGS. 14A-14D. The cylindricalenvelope may be coextensive with a cylindrical structure to limit thespecific distance at which the imaging plane is located relative to theoptical axis between the primary and secondary mirrors. For example, thelocation of the imaging plane may be radially limited by the radius ofthe cylindrical structure.

Light rays impinge upon and are reflected by the primary mirror 304first, the secondary mirror 305 next, the tertiary mirror 313 thirdly,and finally the quaternary mirror 314, so that the rays reach the imageplane 316. The image plane 316 includes one or more sensors, which maybe aggregated in an orderly manner. An entrance pupil of the opticalsystem 300 can be positioned near the primary or the secondary mirrors304, 305. An intermediate focus is formed around a vertex of the primarymirror 304, positioned between the primary and the secondary mirrors304, 305, or between the primary mirror 304 and the tertiary mirror 313.An exit pupil or Lyot stop can be positioned near the quaternary mirror314, between the tertiary and the quaternary mirrors 313, 314, orbetween the quaternary mirror 314 and the image plane 316. As usedherein, a “Lyot stop” has its usual and customary meaning and includes,without limitation, an optical stop that reduces the amount of flarewhich may be caused by diffraction of other stops and baffles in theoptical system. The Lyot stops may be located at images of the system'sentrance pupil and have a diameter slightly smaller than the pupil'simage.

The optical system 300 has a small form factor. The form factor isdefined as the ratio of 1) a distance between the secondary and tertiarymirrors 305, 313 to 2) an effective focal length of the optical system300. The optical system 300 has a form factor of less than 0.2 and of0.09 in some embodiments. The form factor may be from about 0.09 to 0.2,from about 0.04 to less than 0.25. The form factor may be less than0.25. The form factor may have the following values or about thefollowing values: 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.010,0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.20, 0.21, 0.22,0.23, 0.24 or 0.25. The form factor may be less than 0.04, less than0.05, less than 0.06, less than 0.07, less than 0.08, less than 0.09,less than 0.010, less than 0.11, less than 0.12, less than 0.13, lessthan 0.14, less than 0.15, less than 0.16, less than 0.17, less than0.18, less than 0.19, less than 0.20, less than 0.21, less than 0.22,less than 0.23, less than 0.24, or less than 0.25.

In addition to the small form factor, the optical system 300 has abenefit over the prior art in having a much shorter physical distancefrom the tertiary mirror 313 to the image plane 316. The prior art hasquite a long distance between the tertiary mirror and image plane andmandates one or more folding mirrors to fit into a limited dimension.This configuration may lead to difficulty in optical alignment, thermalinstability during operation, which may end with performancedegradation. The optical system 300, because of the small form factorand the short distance between the tertiary mirror 313 and the imageplane 316, eliminates unnecessary folding mirrors and simplifies thealignment and assembly and stability of operation.

The optical system can be designed to have mirrors of zero coefficientof thermal expansion (CTE) materials (such as Zerodur, Fused Silica,Suprasil, Astrostiall, etc.), low-CTE materials (such as Borosilicateglass, like BOROFLOAT, Pyrex, etc.), and mild-CTE materials (such asCrown glass, like NBK7).

For CTE matching, a specific combination of mirror and structurematerials are used for the optical system. Super-invar, invar, ordesigned composite material can be used for zero-CTE mirror materials.Invar, Kovar, ceramics, or designed composite material can be used forlow-CTE mirror materials. Titanium, ceramics, or design compositematerials can be used for mild-CTE mirror materials.

A monolithic structure can be used for the optical system as an ultimatesolution. Mirrors and structures can be made of one material, includingaluminum, ceramics, designed composite materials, and is not limited tothis list.

Referring to FIG. 4 , a schematic of another embodiment of anall-reflective optical system 400 is shown. The optical system 400includes a primary mirror 404, a secondary mirror 405, a tertiary mirror413, a quaternary mirror 414, and image plane 416. The primary mirror404, secondary mirror 405, tertiary mirror 413, the quaternary mirror414 and image plane 416 may have the same or similar features and/orfunctions as, respectively, the primary mirror 304, the secondary mirror305, the tertiary mirror 313, the quaternary mirror 314 and image plane316 of the optical system 300, and vice versa.

However, in the optical system 400, the quaternary mirror 414 is locatedbehind the primary mirror 404, but close to an aperture 410 in theprimary mirror 404. The tertiary mirror 413 is positioned further behindthe primary mirror 404 in the optical system 400 than in the opticalsystem 300. In certain embodiments, the tertiary mirror 413 may bepositioned a distance behind the primary mirror 404 that is in a rangeof 20% to 60%, of 30% to 50%, or of 35% to 45%, of the diameter of theprimary mirror 404. The primary mirror 404 of the optical system 300 inFIG. 3 can be manufactured in one body with the tertiary mirror 313 sothat the center of mass is closer to the primary mirror 304 and thecrosstalk moment of inertia (MOI) of the system can be reduced. Theoptical system 400 of FIG. 4 is different from the optical system 300with regard to effective focal length and field-of-view. An advantage ofthe configuration of the optical system 400 is that placing thequaternary mirror 414 closer to the primary mirror 404 may make iteasier to set a Lyot stop on the quaternary mirror 414 and the centralhole size or aperture 410 of the primary mirror can be minimized.

Referring to FIG. 5 , a schematic of another embodiment of anall-reflective optical system 500 is shown. The optical system 500includes a primary mirror 504, a secondary mirror 505, a tertiary mirror513, a quaternary mirror 514, and an image plane 516. The primary mirror504, secondary mirror 505, tertiary mirror 513, quaternary mirror 514and image plane 516 may have the same or similar features and/orfunctions as, respectively, the primary mirror 304, the secondary mirror305, the tertiary mirror 313, the quaternary mirror 314 and the imageplane 316 of the optical system 300, and vice versa.

However, in the optical system 500, the quaternary mirror 514 is locateda distance behind the primary mirror 504 that is greater than a distancebetween the quaternary mirror 414 and the primary mirror 404 of theoptical system 400 (see FIG. 4 ). Further, in the optical system 500,the tertiary mirror 513 is positioned a distance behind the primarymirror 504 that is greater than a distance of the respectivecorresponding mirrors of the optical system 400. In certain embodiments,the tertiary mirror 513 may be positioned a distance behind the primarymirror 504 that is in a range of 45% to 55% of the diameter of theprimary mirror 504. The optical system 500 may be designed for muchsmaller pixel sensors, such as having a pixel size of less than 4micrometers in certain embodiments. The optical system 500 may bedifferent from the optical system 300 with respect to effective focallength and field-of-view. In some embodiments, the optical system 500may have a shorter effective focal length and a wider field-of-viewrelative to the optical system 300, which may allow the system 500 toinclude sensors with smaller pixel size. But it may be relatively closerto an aperture 610 in the primary mirror 604. The tertiary mirror 613 issimilarly positioned behind the primary mirror 604 as in the opticalsystem 400. An added folding mirror 615 receives rays from thequaternary mirror 614 and reflects them to the image plane 616, which ispositioned above the folding mirror 615. In certain embodiments, theimage plane 616 is positioned to be above and parallel to the opticalaxis.

Some embodiments of the optical systems may have a longer system opticalpath length between the quaternary mirror 614 and the image plane 616using the folding mirror 615. If the image plane 616 is behind thetertiary mirror 613, the system optical path length is the distancebetween the secondary mirror 605 and the image plane 616. With using thefolding mirror 615, the system optical path length is the distancebetween the secondary mirror 605 and the tertiary mirror 613. The imageplane 616 may be positioned to satisfy the requirement of focal lengthand field-of-view. The configuration of the optical system 600 mayprovide a compact design. Another advantage is that the system 600 mayallow for easier installation of a sensor cooler and a radiating platefor the cooler. Furthermore, in the optical system 600, a sensor for theimage plane can be positioned closer to the primary mirror supportingstructure and the sensor can be held in a more stable way.

Referring to FIG. 7 , another embodiment of an all-reflective opticalsystem 700 having a folding mirror 715 is shown. The optical system 700may have the same or similar features and/or functions as the opticalsystem 600, and vice versa. The optical system 600 includes a primarymirror 704, a secondary mirror 705, a tertiary mirror 713, a quaternarymirror 714, and an image plane 716, which may have the same or similarfeatures and/or functions as, respectively, the primary mirror 604, thesecondary mirror 605, the tertiary mirror 613, the quaternary mirror614, and the image plane 616 of the optical system 600, and vice versa.The quaternary mirror 714 is behind the primary mirror 704, as in theoptical system 600, but is close to an aperture 710 in the primarymirror 704. The tertiary mirror 713 is similarly positioned behind theprimary mirror 704 as in the optical system 600. The folding mirror 715receives rays from the quaternary mirror 714 and reflects them to theimage plane 716, which is positioned below the folding mirror 715. Incertain embodiments, the image plane 716 is positioned to be below andparallel to the optical axis. An advantage of the configuration of theoptical system 700 is that the configuration of the mirrors includingthe folding mirror 715 leads to a more compact design. Another advantageis that the optical system 700 can use a sensor for the image plane in alarger package. A CMOS sensor or a sensor with a ROIC tends to havelarger package so that it can embrace more circuits or components thatmay help minimize readout noise, crosstalk, and blooming.

Referring to FIG. 8 , another embodiment of an all-reflective opticalsystem 800 having a folding mirror 815 is shown. The optical system 800may have the same or similar features and/or functions as the opticalsystem 700, and vice versa. The optical system 800 includes a primarymirror 804, a secondary mirror 805, a tertiary mirror 813, a quaternarymirror 814, and an image plane 816, which may have the same or similarfeatures and/or functions as, respectively, the primary mirror 704, thesecondary mirror 705, the tertiary mirror 713, the quaternary mirror714, and the image plane 716 of the optical system 700, and vice versa.However, the image plane 816 is closer to the optical axis than theimage plane 716 is close to its respective optical axis. The quaternarymirror 814 is behind the primary mirror 804 but is further behind itthan in the respective corresponding components of the optical system700. The tertiary mirror 813 is positioned further behind the primarymirror 804 than in the optical system 700. The folding mirror 815receives rays from the quaternary mirror 814 and reflects them to theimage plane 816, which is positioned below the folding mirror 815. Incertain embodiments, the image plane 816 is positioned to be below andparallel to the optical axis. The optical system 800 is designed forsmaller pixel sensors, which are usually commercial or MIL-STD. Anadvantage of the optical system 800 is that it can utilize up-to-datesensors, including commercial or MIL-STD sensors.

Referring to FIG. 9 , another embodiment of an all-reflective opticalsystem 900 having a folding mirror 915 is shown. The optical system 900may have the same or similar features and/or functions as the opticalsystem 800. The optical system 900 includes a primary mirror 904, asecondary mirror 905, a tertiary mirror 913, a quaternary mirror 914,and an image plane 916, which may have the same or similar featuresand/or functions as, respectively, the primary mirror 804, the secondarymirror 805, the tertiary mirror 813, the quaternary mirror 814, and theimage plane 816 of the optical system 800, and vice versa.

However, in the optical system 900, the image plane 916 is closer to theoptical axis than the image plane 816 is close to its respective opticalaxis. The quaternary mirror 914 is behind the primary mirror 904, in asimilar distance to that of the optical system 800. The tertiary mirror913 is positioned behind the primary mirror 904 in a similar distance tothat of the optical system 800. The folding mirror 915 receives raysfrom the quaternary mirror 914 and reflects them to the image plane 916,which is positioned above the folding mirror 915. In certainembodiments, the image plane 916 is positioned to be above and parallelto the optical axis. Advantages of the optical system 900 are that asensor of the image plane can be more stable against vibration and thata cooler with a radiator can be installed in an easier way than in otheroptical system configurations.

Referring to FIG. 10 , an embodiment of an all-reflective optical system1000 having multiple image planes and a folding mirror 1015 is shown.The optical system 1000 may have the same or similar features and/orfunctions as the optical system 600. The optical system 1000 includes aprimary mirror 1004, a secondary mirror 1005, a tertiary mirror 1013, aquaternary mirror 1014, and a first image plane 1016, which may have thesame or similar features and/or functions as, respectively, the primarymirror 604, the secondary mirror 605, the tertiary mirror 613, thequaternary mirror 614 and the image plane 616 of the optical system 600,and vice-versa. The first image plane 1016 is a similar distance to theoptical axis as the image plane 616 is to its respective optical axis.However, optical system 1000 has a second image plane 1016′ similar tothe first image plane 1016. The first image plane 1016 can be dedicatedto a first spectral range and the second image plane 1016′ can bededicated to a second spectral range.

The quaternary mirror 1014 is behind the primary mirror 1004 and isclose to an aperture 1010 in the primary mirror 1004 at a distancesimilar to that in the respective corresponding components of theoptical system 600. The tertiary mirror 1013 is positioned behind theprimary mirror 1004 in a similar distance to that in the respectivecorresponding components of the optical system 600. The folding mirror1015 receives rays from the quaternary mirror 1014 and reflects some ofthe rays within a certain spectral range to the first image plane 1016,which is positioned above the folding mirror 1015. The folding mirror1015 may be transmissive to rays within a second different range fromthat which is reflected. The optical system 1000 enables simultaneousmulti-color imaging by having the folding mirror 1015 be reflective overthe first spectral range and transmissive over the second spectralrange. In certain embodiments, the first image plane 1016 is positionedto be above and parallel to the optical axis, and the second image plane1016′ is positioned to be below and perpendicular to the optical axis onan opposite side of the optical axis as the first image plane 1016. Anadvantage of the optical system 1000 is that it can perform multicolorimaging due to the properties of the folding mirror and the multipleimaging planes.

Referring to FIG. 11 , another embodiment of an all-reflective opticalsystem 1100 having multiple image planes and a folding mirror 1115 isshown. The optical system 1100 may have the same or similar featuresand/or functions as the optical system 1000. The optical system 1100includes a primary mirror 1104, a secondary mirror 1105, a tertiarymirror 1113, a quaternary mirror 1114, a folding mirror 1115 and a firstimage plane 1116, which may have the same or similar features and/orfunctions as, respectively, the primary mirror 1004, the secondarymirror 1005, the tertiary mirror 1013, the quaternary mirror 1014, thefolding mirror 1015 and the first image plane 1016 of the optical system1000, and vice versa. However, in the optical system 1100, the firstimage plane 1116 is positioned at a greater distance to the optical axisthan the first image plane 1016 is to its respective optical axis. Theoptical system 1100 has a second image plane 1116′ similar to the firstimage plane 1116. The first image plane 1116 can be dedicated to a firstspectral range and the second image plane 1116′ can be dedicated to asecond spectral range.

The quaternary mirror 1114 is behind the primary mirror 1104 and isclose to an aperture 1110 in the primary mirror 1104 at a distancesimilar to that in the respective corresponding components of theoptical system 1000. The tertiary mirror 1113 is positioned behind theprimary mirror 1104 in a similar distance to that in the respectivecorresponding components of the optical system 1000. The folding mirror1115 receives rays from the quaternary mirror 1114 and reflects some ofthem to the first image plane 1116, which is positioned below thefolding mirror 1115. The optical system 1100 enables simultaneousmulti-color imaging by having the folding mirror 1115 be reflective overa first spectral range and transmissive over a second spectral range. Incertain embodiments, the first image plane 1116 is positioned to bebelow and parallel to the optical axis, and the second image plane 1116′is positioned to be below and perpendicular to the optical axis. Anadvantage is that the optical system 1100 can use a sensor for the imageplane in a larger package. A CMOS sensor or a sensor with a ROIC tendsto have larger package so that it can embrace more circuits orcomponents that may help minimize readout noise, crosstalk, andblooming.

Referring to FIG. 12 , another embodiment of an all-reflective opticalsystem 1200 having multiple image planes and a folding mirror 1215 isshown. The optical system 1200 may have the same or similar featuresand/or functions as the optical system 1100. The optical system 1200includes a primary mirror 1204, a secondary mirror 1205, a tertiarymirror 1213, a quaternary mirror 1214, a folding mirror 1215 and a firstimage plane 1216, which may have the same or similar features and/orfunctions as, respectively, the primary mirror 1104, the secondarymirror 1105, the tertiary mirror 1113, the quaternary mirror 1114, thefolding mirror 1115 and the first image plane 1116 of the optical system1100, and vice versa. However, in the optical system 1200, the firstimage plane 1216 is positioned at a shorter distance to the optical axisthan the first image plane 1116 is to its respective optical axis. Theoptical system 1200 has a second image plane 1216′ similar to the firstimage plane 1216. The first image plane 1216 can be dedicated to a firstspectral range and the second image plane 1216′ can be dedicated to asecond spectral range.

The quaternary mirror 1214 is behind the primary mirror 1204 at adistance greater than in the respective corresponding components of theoptical system 1100. The tertiary mirror 1213 is positioned behind theprimary mirror 1204 at a greater distance than in the respectivecorresponding components of the optical system 1100. The folding mirror1215 receives rays from the quaternary mirror 1214 and reflects them tothe first image plane 1216, which is positioned below the folding mirror1215. The optical system 1200 enables simultaneous multi-color imagingby having the folding mirror 1215 be reflective over the first spectralrange and transmissive over the second spectral range. In certainembodiments, the first image plane 1216 is positioned to be below andparallel to the optical axis, and the second image plane 1216′ ispositioned to be below and perpendicular to the optical axis. The secondimage plane 1216′ is positioned to be closer to the optical axis thanthe second image plane 1116′ is close to its respective optical axis.The optical system 1200 is designed to utilize smaller pixel sensors forthe image plane. An advantage of the optical system 1200 is that it canutilize up-to-date sensors, including commercial or MIL-STD sensors.

Referring to FIG. 13 , another embodiment of an all-reflective opticalsystem 1300 having multiple image planes and a folding mirror 1315 isshown. The optical system 1300 may have the same or similar featuresand/or functions as the optical system 1000. The optical system 1300includes a primary mirror 1304, a secondary mirror 1305, a tertiarymirror 1313, a quaternary mirror 1314, a folding mirror 1315 and a firstimage plane 1316, which may have the same or similar features and/orfunctions as, respectively, the primary mirror 1004, the secondarymirror 1005, the tertiary mirror 1013, the quaternary mirror 1014, thefolding mirror 1015 and the first image plane 1016 of the optical system1000, and vice versa. However, in the optical system 1300, the firstimage plane 1316 is positioned at a shorter distance to the optical axisthan the first image plane 1016 is to its respective optical axis. Theoptical system 1300 has a second image plane 1316′ similar to the firstimage plane 1316. The first image plane 1316 can be dedicated to a firstspectral range and the second image plane 1316′ can be dedicated to asecond spectral range.

The quaternary mirror 1314 is behind the primary mirror 1304 at adistance greater than in the respective corresponding components of theoptical system 1000. The tertiary mirror 1313 is positioned behind theprimary mirror 1304 at a greater distance than in the respectivecorresponding components of the optical system 1000. The folding mirror1315 receives rays from the quaternary mirror 1314 and reflects them tothe first image plane 1316, which is positioned above the folding mirror1315. The optical system 1300 enables simultaneous multi-color imagingby having the folding mirror 1315 be reflective over the first spectralrange and transmissive over the second spectral range. In certainembodiments, the first image plane 1316 is positioned to be above andparallel to the optical axis, and the second image plane 1316′ ispositioned to be below and perpendicular to the optical axis. The secondimage plane 1316′ is positioned to be closer to the optical axis thanthe second image plane 1016′ is close to its respective optical axis. Anadvantage of the optical system 1300 is that a cooler with a radiatorfor the sensor can be installed in an easier way than in other opticalsystem configurations.

Referring to FIG. 14A, a cross-sectional perspective view of a camerasystem 1400 having an optical system is illustrated. A box 1410illustrates enclosing of the camera and can be a mechanical interface toa satellite BUS. A metering structure 1418, shown as a cone shapedstructure, maintains a distance between a primary mirror 1404 and asecondary mirror 1405. The metering structure 1418 may maintain thisdistance within one micrometer when a temperature changes by 1° C.degree. A supporting structure 1408, best shown as a cylindrical tube inFIG. 14D, supports the primary mirror 1404. In certain embodiments, theradius of the cylindrical structure 1408 can be defined by a radius fromthe portion of the optical axis extending between the primary mirror1404 and the secondary mirror 1405. The inner surface of the curvedsidewall of the cylindrical structure 1408 can be a limit of thespecific distance from the optical axis for the image plane 316described above.

In certain embodiments, dimensions of the camera are 200 mm×200 mm×250mm. Depending on the focal length of an optical system, the dimensionsmay range from 75 mm×75 mm×100 mm, designed for 5 m resolution at 500km, to dimensions of 750 mm×750 mm×1000 mm, designed for 0.25 mresolution at 500 km. The overall volumetric envelope of the camerasystem may be less than 0.01 m3, less than 0.008 m3, less than 0.006 m3,less than 0.004 m3, less than 0.003 m3, less than 0.001 m3, or from0.0005 m3 to 0.01 m3.

The form factor is defined as the ratio of a distance between thesecondary and tertiary mirror to a focal length of the optical system.The distance between the secondary and tertiary mirror may be measuredalong the optical path. In certain embodiments, the optical system canbe implemented in a form factor having the values described above, forexample of less than 0.2, less than 0.15, or less than 0.1. For theprior art, the form factor is known to be more than 0.25. With therelatively smaller form factor of the optical systems described herein,the optical system can provide imaging resolution better than 1 m, 0.5m, or 0.25 m at 500 km altitude. The optical system can also be capableof imaging resolution better than 0.1 m in an elliptical orbit. In otherembodiments, the form factor can be in a range between 0.04 and 0.09.Examples of focal lengths, distances between the secondary mirror andthe tertiary mirror for each focal length and a corresponding formfactor of the system are provided in Table 2.

TABLE 2 Focal Distance between the secondary Form Factor (Distance/Length (mm) mirror and the tertiary mirror (mm) Focal Length) 2300 3400.15 2600 245 0.09 2700 250 0.09 2750 143 0.05 2850 260 0.09 2900 3000.10 3300 200 0.06 3575 300 0.08 3600 300 0.08 3600 260 0.07 3850 3550.09 4000 265 0.07 4000 240 0.06 4000 275 0.07 4500 375 0.08 4650 3750.08 5000 365 0.07 5150 295 0.06 5200 355 0.07 5300 630 0.12 5300 2750.05 5500 355 0.06 5750 325 0.06 6250 675 0.11 7150 390 0.05 7500 4000.05 8500 770 0.09 9000 460 0.05 20000 775 0.04

Referring to FIG. 14B, an embodiment of an optical system 1430 forcameras is illustrated. A metering structure 1448, shown as a coneshaped structure, keeps a distance between a primary mirror 1434 and asecondary mirror 1435 to the design within +/−one micrometer when atemperature changes by one Celsius degree.

For thermal controlling of the metering structure, temperature sensorsand heaters (wire or patch type) can be installed on the meteringstructure. Payload control electronics reads the data from thetemperature sensors and control the heaters to keep the meteringstructure 1448 within a specified range so that the focus of the camerasystem is on aggregated sensors.

A ring structure 1440 is a supporting structure for the primary mirror1434 and supports the primary mirror kinematically so as to minimizestructural distortion that may be induced during assembly. Also, thering structure 1440 can be an interface to a satellite BUS, which caneliminate the need of a box-type enclosure, such as the enclosure 1410shown in FIG. 14A.

Referring to FIG. 14C, a partial cross-sectional perspective view of anoptical system 1460 for cameras is illustrated. A metering structure1478, shown cone-shaped, maintains a distance between a primary mirror1464 and a secondary mirror 1465, which may be maintained in someembodiments within ±one micrometer when a temperature of the meteringstructure 1478 changes by one Celsius degree. The supporting structure1470, shown as a ring-shaped structure, for the primary mirror 1464supports a primary mirror kinematic mounting structure 1472 so as tominimize structural distortion that may be induced during assembly.Also, the supporting structure 1470 can be an interface to a satelliteBUS. In certain embodiments, the radius of the supporting structure 1470can be defined by a physical radius from the optical axis of the primarymirror 1464. The inner surface of the ring structure 1470 can be a limitof the specific distance from the optical axis for the image plane 316described above. A diameter of the primary mirror 1464, which is about7% of the focal length of the optical system, determines a width andheight of the camera system. The length of the camera system isdetermined by the distance between the secondary mirror 1465 and atertiary mirror, which is about 4 to 9% of the focal length of theoptical system.

FIG. 14D is a partial cross-sectional perspective view of an opticalsystem 1480 showing the cylindrical housing 1408 having a radius 1486equal to the radius of the primary mirror 1404. The imaging plane may belocated a radial distance from the optical axis that is no more theradius 1486. The housing 1408 may thus also have the same or nearly thesame radius as the primary mirror for space savings. The optical axisextends between vertices of the primary and secondary mirrors.

Performance

The performance of the optical system 100 and the optical system 150 wasanalyzed to assess its design Modulation Transfer Function (MTF),tolerance MTF, and its distortion. Even though MTF and distortion is away to evaluate optical performance of the system, they also indicatehow the quality of resulting images will be. The MTF of panchromaticband is lower than other big camera systems, which cannot be avoided dueto its smaller aperture size. Despite the lower MTF values, imagequality can be enhanced by post processing on ground and also benefitsby having a smaller anti-aliasing effect.

Referring to FIGS. 15A and 15B, the graphs present the optical designMTF and tolerance MTF, respectively, of the panchromatic band for theoptical system 100. The Nyquist frequencies at which the MTF values areestimated are 100 mm/cycle for the panchromatic band and 25 mm/cycle forthe multispectral bands. For tolerancing, sensitivity of each componentis studied with assembly and alignment logics considered.

Referring to FIGS. 16A and 16B, the graphs present the optical designMTF and tolerance MTF, respectively, of the near-infrared (NIR) band forthe optical system 100. Referring to FIGS. 17A and 17B, the graphspresent the optical design MTF and tolerance MTF, respectively, of theblue band for the optical system 100.

The estimated MTF values of optical system 100 are summarized in Table3. For panchromatic band, the design MTF is higher than 11% andtolerance value is slightly above 10%. For multispectral bands, thedesign values are greater than 57% and tolerance values are better than51%. With tolerancing, MTF drop is higher in multispectral bands becausethose are located away from optical axis with their lower samplingfrequency reflected.

TABLE 3 Spectral bands Design MTF (%) Tolerance MTF (%) PAN (450~720 nm)≥11 ≥10 NIR (770~890 nm) ≥57 ≥51 RED (630~690 nm) ≥63 ≥55 GREEN (520~590nm) ≥68 ≥57 BLUE (450~520 nm) ≥72 ≥59

Referring to FIGS. 18A and 18B, the graphs present the analysis resultsof optical design MTF and tolerance MTF, respectively, of thepanchromatic band for the optical system 150. In a similar manner as forthe optical system 100, the Nyquist frequencies are 100 mm/cycle for thepanchromatic band and 25 mm/cycle for the multispectral bands.Sensitivity of each component was studied and fed into the analysis withassembly and alignment logics considered.

Referring to FIGS. 19A and 19B, the graphs present the optical designMTF and tolerance MTF, respectively, of the NIR band for the opticalsystem 150. Referring to FIGS. 20A and 20B, the graphs present theoptical design MTF and tolerance MTF, respectively, of the blue band forthe optical system 150.

The estimated MTF values of the optical system 150 are summarized inTable 4. The design MTF of the panchromatic band is higher than 15% andthe tolerance value is greater than 14%. For the multispectral bands,the results are different from the optical system 100. Due to the widefield-of-view (FOV) and their location in the FOV, the MTF drops arestrange and get much harsher than for the optical system 100. The lowestmultispectral MTF value is just above 40% at the outer field andsurprisingly at the near-infrared band, which is located closer tooptical axis. The tolerance values are managed to be higher than 35%.

TABLE 4 Spectral bands Design MTF Tolerance MTF PAN (450~720 nm) ≥15 ≥14NIR (770~890 nm) ≥40 ≥35 RED (630~690 nm) ≥46 ≥41 GREEN (520~590 nm) ≥49≥44 BLUE (450~520 nm) ≥53 ≥46

Referring to FIGS. 21A and 21B, the distortion performance of theoptical system 100 and the optical system 150, respectively, isillustrated. The distortion magnitude of the optical system 150 is 0.08micrometer, higher than that of the optical system 100, 0.02 micrometerat the edge, due to its larger field of view. But it should be notedthat the distortion magnitudes of both camera systems are still muchlower than 1/50 pixels, which leads to enough margin for TDI imaging andindicates much less probability of image quality degradation.

Despite having a small form factor, the optical system 100 hasperformance better than other camera systems in constellation operationas shown in Table 5. The optical system 100 is designed to have a groundsample distance of 0.9-meter and a swath-width of 10.8 kilometer at 500kilometer altitude, which are comparable to or better than those ofSKYSAT. It should be also highlighted that the optical system 100 canoperate a panchromatic band and a near-infrared band simultaneously onthe fly, which are optimized compatible with other remote sensingmissions and the other cameras identified in Table 5 are lacking.

TABLE 5 Parameters Optical system 100 SKYSAT^([12]) BLACKSKY^([5])CARBONITE-2^([11]) Orbit Altitude (km) 500 500 450 550 PAN GSD (m) ≤0.9≤0.9 ≤1 ≤1.2 Spectral bands PAN, RGB, NIR RGB, NIR PAN, Color ColorSwath width (nadir, km) ≤10.8 ≤8 ≤6.6 ≤5.9 Clear Aperture (mm) ≤195 ≤350≤240 ≤250 Length (mm) ≤300 — — — Video imaging NA Available NA Available

The benefits of the optical system 150 over DOVE cameras are betterresolution, diverse spectral bands and shorter in axial direction asshown in Table 6. At 500 kilometer altitude, the optical system 150 hasa ground sample distance of 1.85 meters, which is half resolution ofDOVE or PLANETSCOPE. The optical system 150 can be equipped with thecustomized spectral bands, which are essential to extract meaningfulspectral information.

TABLE 6 Parameters Optical system 150 DOVE or PS2^([2]) Orbit Altitude(km) 500 475 Ground Sample Distance (m) ≤1.85 ≤3.7 Spectral bands PAN,RGB, NIR Color Swath width (nadir, km) ≤14.8 ≤24.6 Clear Aperture (mm)≤95 ≤90 Length (mm) ≤200 —

Advantages

The optical system is based on the 4-mirror all-reflective opticaldesign and is free from chromatic aberration and distortion. Being freefrom chromatic aberration helps the optical system go beyond the visiblespectral range so it can support imaging in the infrared and UV spectralrange. Being distortion-free helps the optical system to support TDIimaging in orbit and precision metrics in post-processing.

Some of the prior art, especially the less expensive solutions, stillrelies heavily on a combination of lenses and mirrors in a catadioptricdesign, so that limits its application, or its optical design needs berevised from the beginning to adapt to a different spectral range.Furthermore, the catadioptric design does not easily embrace TDIimaging, especially for a wider field of view imaging because ofinherent or residual aberrations.

The form factor is smaller compared to bigger, more massive systems ofthe prior systems. The optical system described herein has a muchsmaller form factor compared to the prior art. It is quite small so thatit can be installed on a small flying object, including CUBESAT,minisatellite, airplane, UAV, drone, or balloon. It can also be onboardflying objects as a secondary or tertiary payload, which helps providediverse missions or more opportunities for missions. The optical systemis small and lightweight so that it helps reduce launch cost andincrease the opportunity of a launch compared to the prior art. Thebenefit stands out when it comes to constellation operation, wherelaunch cost is a driving factor. The optical system can be developed ata lower cost so that it is more affordable than the prior art. Indeveloping the optical system, smaller test equipment and facilities canbe used due to the smaller aperture size. Also, the optical system islightweight, and it can be transported with lower logistics costs.

The developing process of the optical system can be automated moreefficiently compared to the prior art. Developing the prior art, whichis quite bigger, always mandates labor resources, leading to anincreasing budget. For the optical system with its smaller aperture sizeand being lightweight, iterative or repetitive processes or procedurescan be automated, even with affordable equipment. The processes mayinclude optical alignment, optical measurements (such as wavefronterror, modulation transfer function, a focal length, a field of view,instantaneous field of view, distortion, signal to noise ratio), andthose under various conditions. In addition to the financial benefit,the optical system can sustain stability in operation because of shorterphysical distance among mirrors.

The optical system is based on the 4-mirror optical design and providesdesign flexibility that is backed by a degree of freedom of the opticaldesign. With a minimal modification of the optical design, it can beadapted to provide imaging in the modes of starring, scanning orpushbroom, video, stereo, BRDF (Bidirectional Reflectance DistributionFunction), HDR (High Dynamic Range), Polarimetric, or low-light. Theoptical system, based on the 4-mirror optical design, can supportpanchromatic, multispectral, hyperspectral, infrared, and UV imagingwith minimal design modification, mainly due to different pixel sizes.The optical system has a degree of freedom of optical design and cansupport super-resolution, high dynamic range, polarimetric, and otherremote sensing or scientific imaging.

The optical system can support planetary or deep space missions, whichmandates a small form factor for payload selection. The optical systemcan embrace diverse missions because of its affordability and launchopportunity, which may include AI-based imaging. The optical system canbe used for a precision star sensor and a stellar sensor.

The optical system, based on the 4-mirror optical design, can supportsimultaneous multi-color imaging. It can include, for example, but isnot limited to, panchromatic+RGB+near-infrared, visible+infrared(near-infrared, shortwave infrared, mid-wave infrared, or longwaveinfrared), visible+visible, infrared+infrared, UV+visible, orUV+infrared imaging.

The optical system, being of the small form factor, can be onboard thesatellites of a non-imaging mission, like communication satellites (forexample, Starlink of SpaceX). The optical system can also be installedon other imaging satellites, quasi-imaging satellites, like SAR mission,or scientific mission satellites. This functionality potentially leadsto synchronous or asynchronous constellation operation of the opticalsystem, which enhances the temporal resolution of imaging or increasesimaging opportunity. Constellation operation of the prior art tends tomandate substantial fixed cost of expensive satellite and camera system,24/7 operation of a dedicated control station, and non-automatedimage-receiving centers. The optical system enables synchronous orasynchronous constellation operations so that the resources for controland data receiving can be distributed, leading to significantly reducedfixed cost.

While there has been illustrated and described what are presentlyconsidered to be example embodiments, it will be understood by thoseskilled in the art that various other modifications may be made, andequivalents may be substituted, without departing from claimed subjectmatter. Additionally, many modifications may be made to adapt aparticular situation to the teachings of claimed subject matter withoutdeparting from the central concept described herein. Therefore, it isintended that claimed subject matter not be limited to the particularembodiments disclosed, but that such claimed subject matter may alsoinclude all embodiments falling within the scope of the appended claims,and equivalents thereof.

It is contemplated that various combinations or subcombinations of thespecific features and aspects of the embodiments disclosed above may bemade and still fall within one or more of the inventions. Further, thedisclosure herein of any particular feature, aspect, method, property,characteristic, quality, attribute, element, or the like in connectionwith an embodiment may be used in all other embodiments set forthherein. Accordingly, it should be understood that various features andaspects of the disclosed embodiments can be combined with or substitutedfor one another in order to form varying modes of the disclosedinventions. Thus, it is intended that the scope of the presentinventions herein disclosed should not be limited by the particulardisclosed embodiments described above. Moreover, while the inventionsare susceptible to various modifications, and alternative forms,specific examples thereof have been shown in the drawings and are hereindescribed in detail. It should be understood, however, that theinventions are not to be limited to the particular forms or methodsdisclosed, but to the contrary, the invention is to cover allmodifications, equivalents, and alternatives falling within the spiritand scope of the various embodiments described and the appended claims.Any methods disclosed herein need not be performed in the order recited.

The ranges disclosed herein also encompass any and all overlap,sub-ranges, and combinations thereof. Language such as “up to,” “atleast,” “greater than,” “less than,” “between,” and the like includesthe number recited. Numbers preceded by a term such as “approximately”,“about”, “up to about,” and “substantially” as used herein include therecited numbers, and also represent an amount or characteristic close tothe stated amount or characteristic that still performs a desiredfunction or achieves a desired result. For example, the terms“approximately”, “about”, and “substantially” may refer to an amountthat is within less than 10% of, within less than 5% of, within lessthan 1% of, within less than 0.1% of, and within less than 0.01% of thestated amount or characteristic. Features of embodiments disclosedherein preceded by a term such as “approximately”, “about”, and“substantially” as used herein represent the feature with somevariability that still performs a desired function or achieves a desiredresult for that feature.

With respect to the use of substantially any plural and/or singularterms herein, those having skill in the art can translate from theplural to the singular and/or from the singular to the plural as isappropriate to the context and/or application. The varioussingular/plural permutations may be expressly set forth herein for sakeof clarity.

It will be understood by those within the art that, in general, termsused herein, are generally intended as “open” terms (e.g., the term“including” should be interpreted as “including but not limited to,” theterm “having” should be interpreted as “having at least,” the term“includes” should be interpreted as “includes but is not limited to,”etc.). It will be further understood by those within the art that if aspecific number of an introduced embodiment recitation is intended, suchan intent will be explicitly recited in the embodiment, and in theabsence of such recitation no such intent is present. For example, as anaid to understanding, the disclosure may contain usage of theintroductory phrases “at least one” and “one or more” to introduceembodiment recitations. However, the use of such phrases should not beconstrued to imply that the introduction of an embodiment recitation bythe indefinite articles “a” or “an” limits any particular embodimentcontaining such introduced embodiment recitation to embodimentscontaining only one such recitation, even when the same embodimentincludes the introductory phrases “one or more” or “at least one” andindefinite articles such as “a” or “an” (e.g., “a” and/or “an” shouldtypically be interpreted to mean “at least one” or “one or more”); thesame holds true for the use of definite articles used to introduceembodiment recitations. In addition, even if a specific number of anintroduced embodiment recitation is explicitly recited, those skilled inthe art will recognize that such recitation should typically beinterpreted to mean at least the recited number (e.g., the barerecitation of “two recitations,” without other modifiers, typicallymeans at least two recitations, or two or more recitations).Furthermore, in those instances where a convention analogous to “atleast one of A, B, and C, etc.” is used, in general such a constructionis intended in the sense one having skill in the art would understandthe convention (e.g., “a system having at least one of A, B, and C”would include but not be limited to systems that have A alone, B alone,C alone, A and B together, A and C together, B and C together, and/or A,B, and C together, etc.). In those instances where a conventionanalogous to “at least one of A, B, or C, etc.” is used, in general sucha construction is intended in the sense one having skill in the artwould understand the convention (e.g., “a system having at least one ofA, B, or C” would include but not be limited to systems that have Aalone, B alone, C alone, A and B together, A and C together, B and Ctogether, and/or A, B, and C together, etc.). It will be furtherunderstood by those within the art that virtually any disjunctive wordand/or phrase presenting two or more alternative terms, whether in thedescription, embodiments, or drawings, should be understood tocontemplate the possibilities of including one of the terms, either ofthe terms, or both terms. For example, the phrase “A or B” will beunderstood to include the possibilities of “A” or “B” or “A and B.”

Although the present subject matter has been described herein in termsof certain embodiments, and certain exemplary methods, it is to beunderstood that the scope of the subject matter is not to be limitedthereby. Instead, the Applicant intends that variations on the methodsand materials disclosed herein which are apparent to those of skill inthe art will fall within the scope of the disclosed subject matter.

What is claimed is:
 1. An all-reflective optical system, comprising: aconcave primary mirror; a convex secondary mirror; a concave tertiarymirror; a concave quaternary mirror; and at least one image plane.